Hamdache Abderrazaq 1*, Belkacem Mohamed 1, Hannoun Nourredine 2 COMPUTATIONAL FLUID MODELLING OF FLOW AND MASS TRANSFER IN MEMBRANE CHANNEL OF REVERSE OSMOSIS MODULES Hamdache Abderrazaq 1*, Belkacem Mohamed 1, Hannoun Nourredine 2 University of Sciences and Technology H Boumediene B.P. 32 El Alia, 35111 Algiers, Algeria Tel./Fax +213 (21) 24 71 69;*email: usthb.ge@yahoo.fr 1 F.G.M.G.P. Laboratory of Process and Environmental Engineering, Algiers, Algeria; 2 Math Department, Algiers, Algeria. Abstract : The aim of this work is the application of a computational fluid dynamics model for water treatment by reverse osmosis process. The Navier-Stokes and mass transport equations coupled with the appropriate boundary conditions were solved numerically by the finites volume method. At the inlet, the tangential velocity was assumed to be constant while the velocity profile of Berman was used for the normal velocity component (figure 1). The finite volume code is developed using Fortran 90. The wall concentration and permeate flux were directly determined from the numerical solutions. The cell consists of two parallel walls with one being a membrane and the other an impermeable wall. Common simulation conditions are cross-flow velocity of 0.05-0.250 m.s−1 (Re = 10 - 250), feed concentration of 3 – 9 g.l −1 and permeation velocity of 9.7×10−12m. s−1, several simulation with this conditions had been carried out. The results have been validated against classical solutions available in the literature. Simulation results show that the concentration polarization phenomena can be reduced by increasing feed velocity near the membrane surface. The concentration boundary layer grows continuously across the channel length, regardless of the cross flow velocity. Keywords – reverse osmosis, modelling, finite volume. 1.INTRODUCTION : Mass transfer associated with concentration polarization phenomenon in flat reverse osmosis (RO) modules is mainly influenced by both hydrodynamics in the feed channel and solute transport inside the membrane. This subject is addressed in the present work through an integrated approach using finites volume method for the modeling of the fluid phase together with appropriate boundary conditions that take into account the solute transport inside the membrane. Finites volume method is one technique that can incorporate the intricate couplings introduced by flow in complex geometries which include extreme variations in fluid properties between the bulk solution and the membrane wall encountered during membrane filtration. Results presented describe the development of the model, together with model validation and application. Fig. 1: Reverse osmosis flow channel with one membrane wall. 2.MATHEMATICAL MODEL 2.1.Velocity profiles in the membrane flow channel Under the following flow conditions : a steady state filtration, incompressible fluid, no external forces act on the fluid, laminar flow; The governing Navier-Stokes equations are expressed as: Where U, V, ρ, µ and P are x-velocity, y-velocity, solution density, solution viscosity and pressure respectively. 2.2. Mass transfer in the membrane flow channel Steady state two-dimensional convection-diffusion equation is written as: Where D and C are diffusivity and concentration respectively 2.3.Boundary conditions - A plug flow velocity and a uniform inflow concentration was applied at the inlet  u(x = 0, y) = U0, v(x = 0, y) = 0 , C(x = 0, y) = C0 - At the walls, the no slip condition is imposed and the normal derivative of the concentration is set to zero. u = 0, v = 0, ∂C/∂Y=0. - At membrane surface, velocity and salt concentration are coupled. u = 0, Vw = A(∆P-∆π(Cw, Cp)), D(∂C/∂Y)=Vw(Cw - Cp) Where A and ∆π are permeability and osmotic pressure; ∆P and Cp are applied pressure and permeate concentration. - At the outlet, all derivatives in the flow direction are set to zero. Fig.2: X-Velocity field in the flow direction transition region in an empty channel. Fig.3: Y-Velocity field in the flow direction transition region in an empty channel. Fig.4: Contour plot of dimensionless pressure in an empty channel. Fig.5: Wall concentration along the channel at different inlet velocity . 3. Numerical simulation by finites volumes method Analytical solutions to the convection diffusion mass transfer equation and momentums equations are very difficult to obtain. Numerical simulation may be the method of choice. Different searchers have attempted to solve equation numerically by finites volumes method to predict the concentration profile within the flow channel. This procedure ensures that the physical boundary surfaces coincide with the faces of the boundary control volumes. The transport equations, together with the appropriate boundary conditions, were solved by the control volume approach, with recourse to the SIMPLER algorithm to deal with the pressure-velocity coupling. The convective terms of the transport equations were discretised using the POWER LOW scheme, the algebraic equations resulting from the control volume integration were solved by the BICGSTAB method. 4. RESULTS AND DISCUSSION 4.1. Modeling the velocity profile. In an empty RO feed channel, the parabolic velocity profile in most parts of the channel would be similar to that in a channel with impermeable walls. But in the thin layer near the membrane surface, dominant flow changes from cross flow to flow towards the membrane surface due to permeation, as shown in figures 2 and 3. 4.2.Pressure drop. Pressure drop is an unavoidable phenomenon in the spacer filled channel. The degree of pressure drop in this confined obstructed channel is dependent on the feed Reynolds number. The static dimensionless pressure profile is shown on figure 4 . 4.3. Inlet velocity impact. The concentration profiles (figure 5) clearly show the influence of the cross flow velocity on the concentration polarization (CP) layer. At higher velocities, the CP layer is reduced due to the greater shear effect that diminishes the polarization layer along the whole channel. It is visibly clear from the concentration profiles that both concentration at the membrane surface (Cm) and permeate velocity (Vw), as shown on figure 6, are smaller as U0 increases, for every distance from the inlet. Fig.6: Permeate velocity along the channel at differents inlet velocity . CONCLUSION : Simulation results show that the concentration polarization phenomena can be reduced by increasing feed velocity near the membrane surface. The concentration boundary layer and wall concentration grows continuously across the channel length, regardless of the cross flow velocity, Permeate velocity decrease with increasing wall concentration